US President Donald Trump thanked his supporters, and his Democratic challenger Joe Biden made a final appeal for Americans to vote as polls opened across the United States yesterday.

Election day marked the finale of a tumultuous election season that saw a surge in early voting, legal challenges over ballot counting and, increasingly, fears of violence in the aftermath of the polls.

The country appeared headed for a record-high voter turnout, testament to how fired up the electorate is amid a surging pandemic and after a summer of racial justice protests.

Almost 100 million voters had already cast their votes before election day by mail or in person through early voting, more than 70 per cent of the total in 2016.

That election had set the current record of 139 million people voting. Some 240 million Americans are eligible to vote this year, out of a population of about 330 million.

In a tweet yesterday, Mr Trump thanked his supporters and said he would never let them down.

"Your hopes are my hopes, your dreams are my dreams, and your future is what I am fighting for every single day!" he wrote.

Mr Biden, meanwhile, rallied his supporters to go out and vote.

"In 2008 and 2012, you placed your trust in me to help lead this country alongside Barack Obama. Today, I'm asking for your trust once again - this time, in Kamala and me," he tweeted, referring to his running mate Kamala Harris.

"We can heal the soul of this nation - I promise we won't let you down," he added.

Both candidates spent the eve of the election making a final push in key swing states - mostly Midwestern ones which Mr Trump won by razor-thin margins in 2016 - that could push either of them over the threshold of 270 electoral votes needed to win the White House.

Mr Trump did a whirlwind five rallies in the four battleground states of North Carolina, Pennsylvania, Michigan and Wisconsin, telling supporters that he would win and warning of violence from the losing side.

"Biden's far-left supporters are threatening to loot and rob tomorrow if they don't get their way," he said, adding they would be harshly prosecuted.

Mr Biden held three events in Pennsylvania and one in Ohio, slamming Mr Trump's divisive presidency and promising to get the Covid-19 outbreak under control.

America recorded its second-highest single-day total of more than 91,300 new cases on Monday, as the virus surged in the same Midwestern states that Mr Trump needs to win. "We are going to beat this virus. We are going to get it under control. And the first step to beating this virus is to beat Donald Trump," said Mr Biden.

Though Mr Biden is favoured to win, things are still very much up in the air. The latest opinion polls continue to have Mr Biden ahead of Mr Trump nationally, but his lead has narrowed slightly, with the race tightening in some key battleground states.

As at Monday, Mr Biden had a 6½- to eight-point advantage over Mr Trump nationwide, a margin of around one point down from seven days earlier, according to RealClearPolitics and FiveThirtyEight. Both men are tied in Arizona and North Carolina, according to a Reuters-Ipsos poll that also showed Mr Biden edging ahead in Florida.

A Quinnipiac poll also showed a narrow Biden lead in Florida as well as Ohio, while a Monmouth University poll found Mr Biden's edge in Pennsylvania had narrowed.

Mr Trump told supporters in North Carolina: "We're going to win Florida. If we win Pennsylvania, we win the whole thing."

Both parties are also battling over which ballots should be counted. On Monday, a federal judge ruled against a Republican push to reject 127,000 ballots cast in drive-through tents over the past few days in Harris County, Texas, a Democratic-leaning county in an otherwise red-leaning state.

On Monday, Mr Trump criticised an earlier Supreme Court decision allowing mail-in ballots in Pennsylvania and North Carolina to be received and counted after election day, as long as they were postmarked by election day.

"It will allow rampant and unchecked cheating and will undermine our entire systems of laws.

"It will also induce violence in the streets. Something must be done!" said Mr Trump in a tweet that was marked as misleading by Twitter.

But the prospect of unrest has the nation on edge. Stores were boarded up with plywood in cities from Washington to Manhattan.

States, including Massachusetts and Oregon, put their National Guard on standby in case post-election protests turn violent.

Whether a winner will be called on election night may depend on how close the contest is, although candidates may declare victory before it becomes a certainty.

Mr Trump has urged that votes received after yesterday not be counted, and Axios reported on Sunday that Mr Trump may declare victory on Tuesday night if it looks like he is ahead.

The Biden campaign said in a briefing on Monday that "under no scenario" would Mr Trump be declared victor on election night, arguing that Mr Biden had more pathways to the presidency.

"There is no historical precedent that any of our elections have ever run and been counted and completely verified on election night. We do not expect that to happen in 2020,"said Mr Biden's campaign manager Jennifer O'Malley Dillon.

For live updates and results, follow our US election live coverage.